If hyperbola `(x^(2))/(b^(2))-(y^(2))/(a^(2))=1` passes through the foci of ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`, then find the eccentricities of ellipse and hyperbola.

If hyperbola (x^2)/(b^2)-(y^2)/(a^2)=1 passes through the focus of ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then find the eccentricity of hyperbola.

Find the area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 .

Find the length of Latus rectum of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 .

If x/a+y/b=sqrt(2) touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then find the eccentric angle theta of point of contact.

The eccentricity of ellipse (x^(2))/(25)+(y^(2))/(9)=1 is ……………. .

If the area of the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 is 4pi , then find the maximum area of rectangle inscribed in the ellipse.

(1) Draw the rough sketch of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 . Find the area enclosed by the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 .

The sides A Ca n dA B of a A B C touch the conjugate hyperbola of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 . If the vertex A lies on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then the side B C must touch (a)parabola (b) circle (c)hyperbola (d) ellipse

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is 2 (b) sqrt(2) (c) 3 (d) sqrt(3)

Statement 1 : If from any point P(x_1, y_1) on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, then the corresponding chord of contact lies on an other branch of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.